This study investigates GH(2)/LOX coaxial jet flame at trans- and supercritical conditions using the Reynolds averaged Navier-Stokes approach. Four two-equation-turbulence models, three real equation of states, two chemical mechanisms, and three different chamber pressures are examined. Predictions show good agreement with measurements qualitatively and quantitatively. Based on the results, the predictions of the Soave-Redlich-Kwong equation of state (EOS) are closer to the experiment, while the Aungier-Redlich-Kwong EOS has more deviation than the others. Moreover, the k-omega shear stress transport model has better performance than the other turbulence models. It is also found that the flow field is controlled by two vortices which resulted from extreme expansion of the oxygen dense core and high velocity of inlet gaseous hydrogen into the chamber. The chamber pressure increment delays transcritical conditions and also increases flame length and the length of the secondary vortex and decreases the expansion zone. Furthermore, the two detailed chemical mechanisms of Burke and Konnov had a similar result.